#### Vol. 6, No. 4, 2013

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Irreducible divisor simplicial complexes

### Nicholas R. Baeth and John J. Hobson

Vol. 6 (2013), No. 4, 447–460
##### Abstract

For an integral domain $D$, the irreducible divisor graph ${G}_{D}\left(x\right)$ of a nonunit $x\in D$ gives a visual representation of the factorizations of $x$. Here we consider a higher-dimensional generalization of this notion, the irreducible divisor simplicial complex ${S}_{D}\left(x\right)$. We show how this new structure is a true generalization of ${G}_{D}\left(x\right)$, and show that it often carries more information about the element $x$ and the domain $D$ than its two-dimensional counterpart.

##### Keywords
factorization, simplicial complex
Primary: 13A05
Secondary: 55U10